Logic Programming in a Fragment of Intuitionistic Linear Logic: Extended Abstract

Logic Programming in a Fragment of Intuitionistic Linear Logic: Extended Abstract (1991)

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by Joshua S. Hodas , Dale Miller

Venue:	In Kahn, G. (Ed.), Sixth Annual Symposium on Logic in Computer Science
Citations:	283 - 36 self

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Datum	Value	Source
TITLE	Logic Programming in a Fragment of Intuitionistic Linear Logic: Extended Abstract	INFERENCE
AUTHOR NAME	Joshua S. Hodas	SVM HeaderParse 0.2
AUTHOR AFFIL	Computer Science Department; Harvey Mudd College	SVM HeaderParse 0.2
AUTHOR ADDR	Claremont, CA 91711-5990 USA	SVM HeaderParse 0.2
AUTHOR NAME	Dale Miller	SVM HeaderParse 0.2
AUTHOR AFFIL	Computer Science Department; University of Pennsylvania	SVM HeaderParse 0.2
AUTHOR ADDR	Philadelphia, PA 19104-6389 USA	SVM HeaderParse 0.2
ABSTRACT	When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses. Attempting to prove a goal of the form D ⊃ G from the context (set of formulas) Γ leads to an attempt to prove the goal G in the extended context Γ ∪ {D}. Thus during the bottom-up search for a cut-free proof contexts, represented as the left-hand side of intuitionistic sequents, grow as stacks. While such an intuitionistic notion of context provides for elegant specifications of many computations, contexts can be made more expressive and flexible if they are based on linear logic. After presenting two equivalent formulations of a fragment of linear logic, we show that the fragment has a goal-directed interpretation, thereby partially justifying calling it a logic programming language. Logic programs based on the intuitionistic theory of hereditary Harrop formulas can be modularly embedded into this linear logic setting. Programming examples taken from theorem proving, natural language parsing, and data base programming are presented: each example requires a linear, rather than intuitionistic, notion of context to be modeled adequately. An interpreter for this logic programming language must address the problem of splitting contexts; that is, when attempting to prove a multiplicative conjunction (tensor), say G1 ⊗ G2, from the context ∆, the latter must be split into disjoint contexts ∆1 and ∆2 for which G1 follows from ∆1 and G2 follows from ∆2. Since there is an exponential number of such splits, it is important to delay the choice of a split as much as possible. A mechanism for the lazy splitting of contexts is presented based on viewing proof search as a process that takes a context, consumes part of it, and returns the rest (to be consumed elsewhere). In addition, we use collections of Kripke interpretations indexed by a commutative monoid to provide models for this logic programming language and show that logic programs admit a canonical model. 1	SVM HeaderParse 0.2
YEAR	1991	INFERENCE
VENUE	In Kahn, G. (Ed.), Sixth Annual Symposium on Logic in Computer Science	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	32	INFERENCE
CITATIONS	42 found	ParsCit 1.0